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A052748 Expansion of e.g.f.: -(log(1-x))^3.

%I A052748 #25 Jul 27 2020 16:46:07
%S A052748 0,0,0,6,36,210,1350,9744,78792,708744,7036200,76521456,905507856,
%T A052748 11589357312,159580302336,2352940786944,36994905688320,
%U A052748 617953469022720,10929614667747840,204073497562936320,4011658382046919680,82822558521844224000,1791791417179298304000
%N A052748 Expansion of e.g.f.: -(log(1-x))^3.
%C A052748 Original name: A simple grammar.
%H A052748 Andrew Howroyd, <a href="/A052748/b052748.txt">Table of n, a(n) for n = 0..200</a>
%H A052748 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=704">Encyclopedia of Combinatorial Structures 704</a>
%F A052748 E.g.f.: log(1/(1-x))^3.
%F A052748 Recurrence: {a(1)=0, a(0)=0, a(2)=0, a(3)=6, (-1 - 3*n - 3*n^2 - n^3)*a(n+1) + (9*n + 7 + 3*n^2)*a(n+2) + (-6 - 3*n)*a(n+3) + a(n+4)}.
%F A052748 a(n) = stirling1(n, 3)*3!*(-1)^(n+1). - _Leonid Bedratyuk_, Aug 07 2012
%F A052748 a(n) = 6*A000399(n). - _Andrew Howroyd_, Jul 27 2020
%p A052748 spec := [S,{B=Cycle(Z),S=Prod(B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052748 with(combinat):seq(stirling1(j, 3)*3!*(-1)^(j+1), j=0..50); # _Leonid Bedratyuk_, Aug 07 2012
%o A052748 (PARI) a(n) = {3!*stirling(n,3,1)*(-1)^(n+1)} \\ _Andrew Howroyd_, Jul 27 2020
%Y A052748 Column k=3 of A225479.
%Y A052748 Cf. A000399, A052517.
%K A052748 easy,nonn
%O A052748 0,4
%A A052748 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052748 Name changed and terms a(20) and beyond from _Andrew Howroyd_, Jul 27 2020